1

I have 3 cubic Bézier curves with different control points:

  1. https://cubic-bezier.com/#.17,.8,.77,1 enter image description here
  2. https://cubic-bezier.com/#.18,.59,.5,1 enter image description here
  3. https://cubic-bezier.com/#.12,.41,.41,1 enter image description here

They look similar to each other. Assuming the anchor points $P_0=(0, 0)$, $P_3=(1, 1)$ are static, Is there a way to move $P_1$, $P_2$ while keeping the curve invariant?

Bernard
  • 175,478
zhangxaochen
  • 345

1 Answers1

1

A cubic Bezier curve is defined by the 4 control points. Any change to any control point will result in a different curve. So, moving $P_1$ or $P_2$ while keeping $P_0$ and $P_3$ unchanged will still change the curve.

fang
  • 3,570
  • My original question is edited, there is one more Q: if invariant is impossible, how to keep the deformation as little as possible (while moving $P_1$, $P_2$ around) ? – zhangxaochen Jul 08 '20 at 01:55
  • When P1 and P2 are moved to new locations (and P0 and P3 are fixed), the curve will have a new shape. This new shape will have a certain deviation to the original shape and such deviations cannot be reduced as you don't have any other control points that you can change. – fang Jul 09 '20 at 01:22